The Swans confirmed the signing of Luciano Narsingh from PSV Eindhoven on Thursday afternoon and it is understood that more new players will follow the Netherlands international to the Liberty Stadium this month.
Clement has been linked with a loan move for Spurs midfielder Carroll and a permanent deal for Norwich full-back Olsson, and the Premier League strugglers are currently in discussions for the pair, according to Swansea's new head coach.
"The two clubs are talking about that possibility. The stage it's at is we are looking to agree the terms," Clement told reporters. "There's an interest there [in Carroll]. It's similar situation to Olsson - the clubs are in talks."
Swansea will attempt to make it back-to-back Premier League wins when they welcome Arsenal on Saturday afternoon.